SciPy

numpy.roots

numpy.roots(p)[source]

Return the roots of a polynomial with coefficients given in p.

The values in the rank-1 array p are coefficients of a polynomial. If the length of p is n+1 then the polynomial is described by:

p[0] * x**n + p[1] * x**(n-1) + ... + p[n-1]*x + p[n]
Parameters :

p : array_like

Rank-1 array of polynomial coefficients.

Returns :

out : ndarray

An array containing the complex roots of the polynomial.

Raises :

ValueError :

When p cannot be converted to a rank-1 array.

See also

poly
Find the coefficients of a polynomial with a given sequence of roots.
polyval
Evaluate a polynomial at a point.
polyfit
Least squares polynomial fit.
poly1d
A one-dimensional polynomial class.

Notes

The algorithm relies on computing the eigenvalues of the companion matrix [R243].

References

[R243](1, 2) R. A. Horn & C. R. Johnson, Matrix Analysis. Cambridge, UK: Cambridge University Press, 1999, pp. 146-7.

Examples

>>> coeff = [3.2, 2, 1]
>>> np.roots(coeff)
array([-0.3125+0.46351241j, -0.3125-0.46351241j])

Previous topic

numpy.poly

Next topic

numpy.polyfit